METRICAL FIXED POINT THEOREMS VIA LOCALLY FINITELY T-TRANSITIVE BINARY RELATIONS UNDER CERTAIN CONTROL FUNCTIONS

被引：34

作者：

Alam, Aftab ^{[1
]}

Arif, Mohammad ^{[1
]}

Imdad, Mohammad ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

来源：

MISKOLC MATHEMATICAL NOTES | 2019年 / 20卷 / 01期

关键词：

locally finitely T-transitive binary relations; control functions; R-connected sets; PARTIALLY ORDERED SETS; GENERALIZED CONTRACTIONS; NONLINEAR CONTRACTIONS; SPACES;

D O I：

10.18514/MMN.2019.2468

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we extend relation-theoretic contraction principle due to Alam and Imdad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T-transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693702), Agarwal et al. (Applicable Analysis, 87 (1) (2008) 109-116), Berzig and Karapinar (Fixed Point Theory Appl. 2013:205 (2013) 18 pp), Berzig et al. (Abstr. Appl. Anal. 2014:259768 (2014) 12 pp) and Turinici (The Sci. World J. 2014:169358 (2014) 10 pp).

引用

页码：59 / 73

页数：15

共 26 条

[1] Generalized contractions in partially ordered metric spaces [J].

Agarwal, Ravi P. ;

El-Gebeily, M. A. ;

O'Regan, Donal .

APPLICABLE ANALYSIS, 2008, 87 (01) :109-116

[2] NONLINEAR CONTRACTIONS IN METRIC SPACES UNDER LOCALLY T-TRANSITIVE BINARY RELATIONS [J].

Alam, Aftab ;

Imdad, Mohammad .

FIXED POINT THEORY, 2018, 19 (01) :13-23

[3] Relation-Theoretic Metrical Coincidence Theorems [J].

Alam, Aftab ;

Imdad, Mohammad .

FILOMAT, 2017, 31 (14) :4421-4439

[4] Relation-theoretic contraction principle [J].

Alam, Aftab ;

Imdad, Mohammad .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2015, 17 (04) :693-702

[5] Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications [J].

Alam, Aftab ;

Khan, Abdur Rauf ;

Imdad, Mohammad .

FIXED POINT THEORY AND APPLICATIONS, 2014,

[6]

Banach S., 1922, Fund. Maths., V3, P133, DOI [DOI 10.4064/FM-3-1-133-181, 10.4064/fm-3-1-133-181]

[7] Discussion on Generalized-(αψ, βφ)-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems [J].

Berzig, Maher ;

Karapinar, Erdal ;

Roldan-Lopez-de-Hierro, Antonio-Francisco .

ABSTRACT AND APPLIED ANALYSIS, 2014,

[8] Fixed point results for -contractive mappings for a generalized altering distance [J].

Berzig, Maher ;

Karapinar, Erdal .

FIXED POINT THEORY AND APPLICATIONS, 2013,

[9]

Boyd D. W., 1969, P AM MATH SOC, V30

[10]

BROWDER FE, 1968, P K NED AKAD A MATH, V71, P27

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